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  • © 1980

Vector Bundles on Complex Projective Spaces

Part of the book series: Progress in Mathematics (PM, volume 3)

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  • ISBN: 978-1-4757-1460-9
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Table of contents (2 chapters)

  1. Front Matter

    Pages N1-vii
  2. Holomorphic Vector Bundles and the Geometry of ℙn

    • Christian Okonek, Michael Schneider, Heinz Spindler
    Pages 1-138
  3. Stability and Moduli Spaces

    • Christian Okonek, Michael Schneider, Heinz Spindler
    Pages 139-373
  4. Back Matter

    Pages 374-389

About this book

These lecture notes are intended as an introduction to the methods of classification of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = Fn. According to Serre (GAGA) the classification of holomorphic vector bundles is equivalent to the classification of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some funda­ mental results from these fields are summarized at the beginning. One of the authors gave a survey in the Seminaire Bourbaki 1978 on the current state of the classification of holomorphic vector bundles overFn. This lecture then served as the basis for a course of lectures in Gottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the introductory nature of this book we have had to leave out some difficult topics such as the restriction theorem of Barth. As compensation we have appended to each sec­ tion a paragraph in which historical remarks are made, further results indicated and unsolved problems presented. The book is divided into two chapters. Each chapter is subdivided into several sections which in turn are made up of a number of paragraphs. Each section is preceeded by a short description of iv its contents.

Keywords

  • algebra
  • algebraic geometry
  • geometry
  • Manifold
  • theorem

Authors and Affiliations

  • Mathematische Institut der Universität, Göttingen, Federal Republic of Germany

    Christian Okonek, Michael Schneider, Heinz Spindler

Bibliographic Information

  • Book Title: Vector Bundles on Complex Projective Spaces

  • Authors: Christian Okonek, Michael Schneider, Heinz Spindler

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-1460-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1980

  • Softcover ISBN: 978-1-4757-1462-3

  • eBook ISBN: 978-1-4757-1460-9

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: VII, 389

  • Topics: Probability Theory, Statistics

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-1-4757-1460-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 139.99
Price excludes VAT (USA)